Trigonometric Equations Question 263
Question: If in a $ \Delta ABC,,\angle A=45^{o},\angle C=60^{o} $ , then $ a+c\sqrt{2}= $
[MP PET 1999]
Options:
A) b
B) 2b
C) $ \sqrt{2b} $
D) $ \sqrt{3}b $
Show Answer
Answer:
Correct Answer: B
Solution:
- $ A=45^{o},C=60^{o},A+B+C=\pi \Rightarrow B=75^{o} $
Þ $ a+c\sqrt{2}=k\sin A+k\sin C(\sqrt{2}) $ $ =k\sin 45^{o}+\sqrt{2}k\sin 60^{o} $ $ =2k( \frac{\sqrt{3}+1}{2\sqrt{2}} )=2k\sin 75^{o}=2k\sin B $ \ $ a+c\sqrt{2}=2b $ .
BETA
